Details

Time bar (total: 11.9s)

sample54.0ms

Algorithm
intervals
Results
19.0ms256×body80valid
17.0ms238×body80nan

simplify63.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
01828
13122
25222
36822
48822
510022
610422
done10422

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot re im)
0.3b
(/ (fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im))))) (fma (log base) (log base) (* 0.0 0.0)))
0.4b
(fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im)))))
0.6b
(fma (log base) (log base) (* 0.0 0.0))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
6×add-exp-log add-cbrt-cube
4×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-/r* associate-/l*
2×fma-udef
1×cbrt-undiv hypot-udef frac-2neg div-exp clear-num div-inv
Counts
4 → 59
Calls
4 calls:
0.0ms
(hypot re im)
2.0ms
(/ (fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im))))) (fma (log base) (log base) (* 0.0 0.0)))
0.0ms
(fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im)))))
0.0ms
(fma (log base) (log base) (* 0.0 0.0))

series409.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(hypot re im)
70.0ms
(/ (fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im))))) (fma (log base) (log base) (* 0.0 0.0)))
34.0ms
(fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im)))))
258.0ms
(fma (log base) (log base) (* 0.0 0.0))

simplify1.1s

Counts
71 → 71
Iterations

Useful iterations: 3 (182.0ms)

IterNodesCost
01051432
11861415
24111233
311861176
done50001176

prune383.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 1 expressions with local error:

0.3b
(/ (atan2 im re) (- (log base)))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
26×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
16×distribute-lft-neg-in distribute-rgt-neg-in
12×associate-/r*
9×pow1
8×log-pow
4×neg-mul-1
3×add-exp-log add-cbrt-cube associate-/l*
1×cbrt-undiv expm1-log1p-u frac-2neg div-exp clear-num log1p-expm1-u div-inv add-log-exp
Counts
1 → 65
Calls
1 calls:
4.0ms
(/ (atan2 im re) (- (log base)))

series44.0ms

Counts
1 → 3
Calls
1 calls:
44.0ms
(/ (atan2 im re) (- (log base)))

simplify2.4s

Counts
68 → 68
Iterations

Useful iterations: done (2.4s)

IterNodesCost
0108903
1186857
2389831
3941823
42013823
done5000820

prune198.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 2 expressions with local error:

0.3b
(/ -1 (log base))
0.3b
(* (atan2 im re) (/ -1 (log base)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt times-frac
20×add-cube-cbrt *-un-lft-identity
16×associate-*r*
11×pow1
9×add-exp-log add-cbrt-cube
7×log-pow
4×associate-/r*
3×associate-*l* associate-/l*
2×cbrt-undiv expm1-log1p-u div-exp prod-exp cbrt-unprod log1p-expm1-u div-inv add-log-exp unswap-sqr
1×frac-2neg associate-*r/ pow-prod-down clear-num *-commutative
Counts
2 → 70
Calls
2 calls:
2.0ms
(/ -1 (log base))
11.0ms
(* (atan2 im re) (/ -1 (log base)))

series200.0ms

Counts
2 → 6
Calls
2 calls:
157.0ms
(/ -1 (log base))
43.0ms
(* (atan2 im re) (/ -1 (log base)))

simplify2.3s

Counts
76 → 76
Iterations

Useful iterations: 3 (1.0s)

IterNodesCost
0103741
1208670
2651612
32373604
done5000604

prune224.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (fma 0.0 0.0 (pow (log base) 2)))
0.4b
(fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im)))))
0.4b
(* (fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im))))) (/ 1 (fma 0.0 0.0 (pow (log base) 2))))
0.6b
(pow (log base) 2)

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
23×*-un-lft-identity
22×add-cube-cbrt
20×times-frac
18×add-exp-log
13×associate-*r*
11×add-cbrt-cube
9×pow1
4×expm1-log1p-u unpow-prod-down div-exp prod-exp log1p-expm1-u add-log-exp
3×pow-unpow associate-*l* associate-/r* associate-/l* unswap-sqr
2×cbrt-undiv rec-exp 1-exp cbrt-unprod div-inv
1×pow-to-exp pow-flip pow-pow frac-2neg associate-*r/ pow-prod-down pow-exp clear-num log-pow un-div-inv *-commutative fma-udef unpow2 inv-pow sqr-pow
Counts
4 → 102
Calls
4 calls:
2.0ms
(/ 1 (fma 0.0 0.0 (pow (log base) 2)))
0.0ms
(fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im)))))
8.0ms
(* (fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im))))) (/ 1 (fma 0.0 0.0 (pow (log base) 2))))
2.0ms
(pow (log base) 2)

series465.0ms

Counts
4 → 12
Calls
4 calls:
216.0ms
(/ 1 (fma 0.0 0.0 (pow (log base) 2)))
30.0ms
(fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im)))))
72.0ms
(* (fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im))))) (/ 1 (fma 0.0 0.0 (pow (log base) 2))))
147.0ms
(pow (log base) 2)

simplify1.7s

Counts
114 → 114
Iterations

Useful iterations: 3 (709.0ms)

IterNodesCost
01572015
13271846
27621568
328111548
done50001548

prune393.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0b

regimes261.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
088
1108
done108

end0.0ms

sample1.6s

Algorithm
intervals
Results
598.0ms7982×body80nan
583.0ms8000×body80valid